Aircraft: COMMERCIAL FIXED WING
Phase of flight: Climb
Anomaly: Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance

Departing Runway XXR ZZZ we were filed ZZZ1 Departure ZZZ transition then ZZZZZ [fix]. Upon receipt of CPDLC clearance there was a route modification that was obtained that had us routed via the ZZZZA3 ZZZZZ. I loaded the flight plan per the CDU prompt and accepted the clearance and printed it out. There was plenty of time as loading was delayed. When I reviewed the loaded clearance it came up ZZZZA3 ZZZZA ZZZZZ. I then went back to the DEP/ARR page and checked the runway and SID which I had previously selected to ensure it was still in the FMC. I did notice that the routing had us now going south to ZZZZZ and thought the ZZZZA ZZZZZ was a short cut ATC wanted due to light traffic and time of day. I also looked at the printout and didn't see the period between ZZZZA3 and ZZZZZ as in ZZZZA3 DZZZZZ verses ZZZZA3.ZZZZZ meaning that ZZZZZ was the transition. Once we were airborne ATC cleared us directly to 12;000 which we were initially given 7;000 in the clearance. ATC then came back and said maintain 12;000 unrestricted which in my mind validated the shortcut because usually you get the phraseology 'Climb via the SID except maintain XXX'. ATC then informed us our deviate and asked us if we were on the SID. I said affirmative except from ZZZZA we were direct to ZZZZZ which was incorrect according to the clearance. After getting to cruise the Captain and I discussed the situation looking at both the clearance; the FOM and the loaded routing from the CPDLC. We realized that two errors were made. When I loaded the SID I did not reselect the runway and SID with the ZZZZZ transition because when I checked it was in the box and because we both missed the period in the printout and ZZZZZ was on the regular routing I thought ATC wanted us to cut that part of the SID off because of low traffic volume. It was pilot error and it's a difficult lesson. I am fully aware that a period means a transition but I missed it on the printout and assumed ATC wanted a shorter routing which has become the norm is so many ATC environments with COVID. I also realize that I will always double check every period on the CDU against the printout copy as it's easier to see. In addition I will ensure that every modification in the future requires an input of both the runway and SID even when uploading clearances from CPDLC which I'm aware to do but I didn't see the period on the printout. I take full responsibility for this mistake and I feel really bad I missed such a small but signification part of the clearance. I know better so there's no excuses for this missed detail. First leg (and only leg) with FO; blocked XX mins late for loading; so not rushed. Filed FP was ZZZ1 ZZZ transition; ZZZ [VOR]; ZZZZZ; RXXX ....CPDLC had 'route change' (I was doing exterior prefect when it came): cleared ZZZZA3 ZZZZZ; RXXX ... climb via SID except maintain 7;000 feet. The actual printout was 'ZZZZA3. ZZZZZ'; which means the ZZZZZ transition with the 'dot' in between. We missed that dot. We both assumed the clearance was direct from ZZZZA to ZZZZZ. The ZZZ1 does not have ZZZZZ as a transition; yet it was on our filed flight plan. To add some justification for our assumption; the ZZZ1 goes way north and west before heading west. The ZZZZA SID went south of ZZZ [airport] and more direct west on course. Add that is was [early] in the morning (very light traffic plus Covid19 low traffic) we assumed we were cleared a more direct routing south of ZZZ [airport]. And the Controller gave us climb unrestricted to 12;000 which also made sense for the Direct ZZZZZ we had in the FMC. And then climb to FL340 but then stopped us at 15;000. But we were wrong. He questioned us and we discovered the actual clearance was the entire transition out to ZZZZZ. At that point he cleared us to ZZZZZ and to climb to FL340 again. No TCAS or other traffic was in the area. This was a crew error. We both were very disappointed with the mistake. We reviewed the FOM and saw our mistake. We have both done this correctly many times but the 'ZZZZZ' on the filed route threw us off. No other excuse. And as the Captain I take responsibility. Air carrier flight crew reported a track deviation occurred due to misreading a changed departure clearance.